So I know Lola has to be the same class as any card you want to play but does that specifically denote using the play action? If I play Sleight of Hand or Ever Vigilant, and thus am the required class I would need to be to play the respective card, would I then be able to play down a card outside my class?

My guess is no in the case of Ever Vigilant as its text specifically states you are ' playing up to 3 assets from your hand' and you can not play cards out of your current class and there is no window to class change in the middle of the event.

But that gets a little murkier on Sleight of hand. Sleight of hand tells you to 'p ut an Item asset into play from your hand '. You aren't explicitly playing the card, you're instead playing another card that is putting the the card into play for you and after which you can class change to it so you can actually use it.

So thoughts? Would either allow you to play a card out of your color as Lola?

The rules on Lola can get a bit murky. My thought is that you are correct with regards to Ever Vigilant. You have to be in Guardian class to play it, and the three assets would have to be Guardian or Neutral to play. Sleight of Hand might get around that though because it does say to put an item directly into play.

The distinction between "play" and "put into play" exists in every single LCG FFG ever designed. Effects that apply to one do not automatically apply to the other (they do only if both are specified), so Sleight of Hand (and any card that puts another into play) isn't limited by Lola's role (because you're putting a card into play rather than playing it).